Extra Dimensions in Quantum Newtonian Cosmology

This entry surveys the role of extra dimensions in Newtonian quantum cosmology, with particular emphasis on large, compactified, and warped dimensional geometries and their impact on the Newtonian potential in the early universe. The discussion begins with a review of Kaluza–Klein type toy models, followed by models with large extra dimensions in which gravity propagates into a higher-dimensional bulk, producing Yukawa-like modifications to the inverse-square law at submillimeter scales. Compactification schemes on toroidal and spherical dimensions are then examined, yielding the spectrum of Kaluza–Klein modes and quantifying their corrections to the Newtonian potential. Warped extra dimensions of the Randall–Sundrum type are also considered, in which a warp factor dimension is introduced; the resulting modifications to the Newtonian interaction in quantum-corrected cosmological settings are discussed in detail.